List comprehension in Mathematica

This one is very close to your Python code

Join @@ Table[Append[a, i], {a, A}, {i, Intersection[Range[3], a]}]

{{1, 2, 3, 1}, {1, 2, 3, 2}, {1, 2, 3, 3}, {2, 3, 4, 2}, {2, 3, 4, 3}, {3, 4, 5, 3}}

Some of the other approaches might be much more efficient, but the following shows how one can create something which is probably as easy to read (if one is fluent in Mathematica) as a python list comprehension:

SetAttributes[listComprehend, HoldAll]

listComprehend[Verbatim[Condition][body_, crit_],iters:({_, __}..)] := Flatten[
    Table[
        If[crit, body, Unevaluated[Sequence[]]],
        iterators
    ], 1]

use it like this:

listComprehend[Append[a, i] /; MemberQ[a, i], {a, A}, {i, 3}]

/; is the shortcut for Condition and usually can be read as "provided that" in mathematica code. Doing so, the above seems to be relatively clear code. Unfortunately the translation to one of the potentially more efficient approaches is not that simple...

A = {{1, 2, 3}, {2, 3, 4}, {3, 4, 5}};
Join @@ Table[If[a~MemberQ~i, a~Join~{i}, Unevaluated[]], {a, A}, {i, 3}]
Join @@ Table[a~Join~{i}, {a, A}, {i, Select[Range@3, a~MemberQ~# &]}]

{{1, 2, 3, 1}, {1, 2, 3, 2}, {1, 2, 3, 3}, {2, 3, 4, 2}, {2, 3, 4, 3}, {3, 4, 5, 3}}